Geometric Regularization for Long-Tailed Semi-Supervised Learning via Gaussian Feature Bridges

Real-world semi-supervised learning (SSL) often encounterssignificant challenges with long-tailed label distributions and noisy pseudo-labels, which hinder generalization and amplify confirmation bias. In thiswork, we introduce a novel framework, Gaussian Bridge Consistency(GBC), to address these challenges by constructing semantic interpo-lation paths between unlabeled samples and high-quality class anchors.Our method maintains a dynamic Prototype Atlas that stores a diverseand evolving set of labeled and pseudo-labeled exemplars per class. Foreach unlabeled instance, GBC forms a class-conditional Gaussian Fea-ture Bridge in the latent space, enabling the student model to traversea smooth trajectory from uncertain predictions to reliable class proto-types. A bridge consistency loss is applied along this path to enforcealignment with a geometrically interpolated target distribution. Further-more, we propose BridgeMix, a confidence-aware feature mixing strategythat interpolates both sample and anchor pairs to amplify cross-samplegeneralization. Extensive experiments on CIFAR10-LT and ImageNet-LT (USB benchmarks) validate the robustness and effectiveness of GBCunder realistic long-tailed SSL settings, consistently improving long tail-class performance without sacrificing scalability.